Let’s assume you have taken 100 samples of size 36 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 25.
0.694
To calculate the standard deviation of the sample means, also known as the standard error of the mean, we can use the formula:
Standard error of the mean = population standard deviation / √sample size
In this case, the population variance is given as 25. Since the population standard deviation is the square root of the variance, we can find it by taking the square root:
Population standard deviation = √population variance = √25 = 5
The sample size is given as 36, and the number of samples is given as 100.
Now, we can substitute the values into the formula:
Standard error of the mean = 5 / √36
Simplifying it further:
Standard error of the mean = 5 / 6
Therefore, the standard deviation of the sample means is 5/6 or approximately 0.833.